Question

The three sides of a right triangle have integral lengths which form an AP.Find the length of any one of its sides.

Answer 1

Let 'a' be the length of a side of the triangle. a∈Ζ.
∵The sides are in A.P.
∴The sides are: (a-d),a,(a+d).
By Pythagoras's theorem,

(a-d)² + a² = (a+d) ²
Solving, we get,
a=4d.
∵ The sides of the triangle has integral length. ∴ d∈Ζ.
∴ The sides are 3d,4d,5d. d∈Z.(Putting a=4d). (Ans.)